example of problem solving subtraction

Problem Solving on Subtraction

Problem solving on subtraction will help us to get the idea on how to solve the basic subtraction statement problems.

1. Eight birds sat on a wire. Three birds flew away. How many were left?

Total number of birds sat on a wire = 8

Number of birds flew away = 3

Therefore, number of birds left = 8 - 3 = 5

2. Sam had 7 dollars. He spent 4 dollars. How many dollars is he left with?

Total amount of money Sam had = $7

He spent = $4

Therefore, amount of money left with him = $7 - $4 = $3

3. Five boats were tied up. Four of the boats sailed away. How many were left?

Total number of boats tied up = 5

Number of boats sailed away = 4

Therefore, number of boats were left = 5 - 4 = 1

4. Ron had 10 stamps. His father took 2 stamps. How many stamps does Ron have now?

Total number of stamps Ron had = 10

Number of stamps his father took = 2

Therefore, number of stamps he have now = 10 - 2 = 8

5. Diana had 18 toffees. She gave 5 toffees to her friend. How many toffees left with her?

Total number of toffees Diana had = 18

Number of toffees she gave to her friend = 5

Therefore, number of toffees left = 18 - 5 = 13

More examples on statement problem solving on subtraction:

6. Mr. Daniel had 39 goats in a pasture. When he opened the pasture gate, 13 goats went out. How many goats remained in?

Total number of goats in a pasture Mr. Daniel had = 39

Number of goats went out = 13

Therefore, number of goats remained in = 39 - 13 = 26

7. Derek’s father is 47 years old. His mother is 35 years old. What is the difference of their ages?

Age of Derek’s father = 47 years

Age of his mother = 35 years

Therefore, difference of their ages = 47 - 35 = 12 years

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Subtraction Word Problems (1-step word problems)

These lessons look at some examples of subtraction word problems that can be solved in one step, illustrating the use of bar models or block diagrams in the solution process.

Related Pages 2-step Subtraction Word Problems Using Bar Models Solving Word Problems Using Bar Models Singapore Math More Word Problems

We will illustrate how block diagrams can be used to help you to visualize the subtraction word problems in terms of the information given and the data that needs to be found. The block diagrams or block modeling method is used in Singapore Math.

Example: Jessica has 1135 beads. 604 beads are red and the rest are blue. How many blue beads does she have?

1135 – 604 = 531

She has 531 blue beads.

Example: James and Ken donated $2300 to a charitable organization. Ken donated $658. How much did James donate?

2300 – 658 = 1642 James donated $1642.

Example: The price of a car is $2795 and the price of a motorbike is $1063. What is the difference between the prices of the 2 vehicles?

Solution: 2795 – 1063 = 1732

The difference between the prices of the 2 vehicles is $1732.

Example: There are 967 chairs in a hall. During an event, 761 chairs were occupied. How many chairs were not occupied?

967 – 761 = 206 206 chairs were not occupied.

Examples of subtraction word problems

134 girls and 119 boys took part in an art competition. How many more girls than boys were there?

Mei Lin saved $184. She saved $63 more than Betty. How much did Betty saved?

John read 32 pages in the morning. He read 14 pages less in the afternoon. a) How many pages did he read in the afternoon? b) How many pages did they read altogether?

A visual way to solve world problems using bar modeling This type of word problem uses the part-whole model.

Example: Mr. Oliver bought 88 pencils. he sold 26 of them. How many pencils did he have left?

A visual way to solve world problems using bar modeling This type of word problem uses the part-whole model. Because the part is missing, this is a subtraction problem.

Example: There are 98 hats, 20 of them are pink and the rest are yellow. How many yellow hats are there?

Example: Cayla did 88 sit-ups in the morning. Nekira did 32 sit-ups at night. How many more sit-ups did Cayla do than Nekira?

How to use bar modeling in Singapore math to solve word problems that deal with comparing?

Example: Adam has 11 fewer lollipops than Hope. If Adam has 16 lollipops, how many lollipop does Hope have?

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Subtraction

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

What Is Subtraction?

Subtraction is an operation used to find the difference between numbers . When you have a group of objects and you take away a few objects from it, the group becomes smaller. For example, you bought 9 cupcakes for your birthday party and your friends ate 7 cupcakes. Now you are left with 2 cupcakes. This can be written in the form of a subtraction expression: 9 - 7 = 2 and is read as "nine minus seven equals two". When we subtract 7 from 9, (9 - 7) we get 2. Here, we performed the subtraction operation on two numbers 9 and 7 to get the difference of 2.

Subtraction Symbol

In mathematics, we have different symbols. The subtraction symbol is one of the important math symbols that we use while performing subtraction. In the above section, we read about subtracting two numbers 9 and 7. If we observe this subtraction: (9 - 7 = 2), the symbol (-) connects the two numbers and completes the given expression. This symbol is also known as the minus sign.

Subtraction Formula

When we subtract two numbers, we use some terms which are used in the subtraction expression:

Minuend: The number from which the other number is subtracted.
Subtrahend: The number which is to be subtracted from the minuend.
Difference: The final result after subtracting the subtrahend from the minuend.

The subtraction formula is written as: Minuend - Subtrahend = Difference

Let us understand the subtraction formula or the mathematical equation of subtraction with an example.

Here, 9 is the minuend, 7 is the subtrahend, and 2 is the difference.

How To Solve Subtraction Problems?

While solving subtraction problems, one-digit numbers can be subtracted in a simple way, but for larger numbers, we split the numbers into columns using their respective place values , like Ones, Tens, Hundreds, Thousands, and so on. While solving such problems we may encounter some cases with borrowing and some without borrowing. Subtraction with borrowing is also known as subtraction with regrouping. When the minuend is smaller than the subtrahend, we use the regrouping method. While regrouping, we borrow 1 number from the preceding column to make the minuend bigger than the subtrahend. Let us understand this with the help of a few examples.

Subtraction Without Regrouping

Example: Subtract 25632 from 48756.

Note: In subtraction, we always subtract the smaller number from the larger number to get the correct answer.

Solution: Follow the given steps and try to relate them with the following figure.

Step 1: Start with the digit at ones place. (6 - 2 = 4) Step 2: Move to the tens place. (5 - 3 = 2) Step 3: Now subtract the digits at hundreds place. (7 - 6 = 1) Step 4: Now subtract the digits at thousands place. (8 - 5 = 3) Step 5: Finally, subtract the digits at ten thousands place. (4 - 2 = 2) Step 6: Therefore, the difference between the two given numbers is: 48756 - 25632 = 23124.

Subtraction With Regrouping

Example: Subtract 3678 from 8162.

Solution: Follow the given steps and try to relate them with the following figure. We need to solve: 8162 - 3678 Step 1: Start subtracting the digits at ones place. We can see that 8 is greater than 2. So, we will borrow 1 from the tens column which will make it 12. Now, 12 - 8 = 4 ones. Step 2: After giving 1 to the ones column in the previous step, 6 becomes 5. Now, let us subtract the digits at the tens place (5 - 7). Here, 7 is greater than 5, so we will borrow 1 from the hundreds column. This will make it 15. So,15 - 7 = 8 tens. Step 3: In step 2 we had given 1 to the tens column, so we are left with 0 at the hundreds place. To subtract the digits on the hundreds place, i.e., (0 - 6) we will borrow 1 from the thousands column. This will make it 10. So, 10 - 6 = 4 hundreds. Step 4: Now, let us subtract the digits at the thousands place. After giving 1 to the hundreds column, we have 7. So, 7 - 3 = 4 Step 5: Therefore, the difference between the two given numbers is: 8162 - 3678 = 4484

Subtraction Using Number Line

A number line is a visual aid that helps us understand subtraction because it allows us to jump backward and forward on each number. To understand how this works, let us explore subtraction using a number line. Let us subtract 4 from 9 using a number line. We will start by marking the number 9 on the number line. When we subtract using a number line, we count by moving one number at a time towards the left-hand side. Since we are subtracting 4 from 9, we will move 4 times to the left. The number on which you land after 4 backward jumps, is the answer. Thus, 9 - 4 = 5.

Real Life Subtraction Word Problems

The concept of subtraction is often used in our day-to-day activities. Let us understand how to solve real-life subtraction word problems with the help of an interesting example.

Example: A soccer match had a total of 4535 spectators. After the first innings, 2332 spectators left the stadium. Find the number of remaining spectators.

Solution: Given: The total number of spectators present in the first innings = 4535; The number of spectators who left the stadium after the first innings = 2332 Here, 4535 is the minuend and 2332 is the subtrahend.

Th H T O 4 5 3 5 -2 3 3 2 2 2 0 3

Therefore, the number of remaining spectators = 2203.

Important Notes on Subtraction:

Here are a few important notes that you can follow while performing subtraction in your everyday life.

Any subtraction problem can be transformed into an addition problem and vice-versa.
Subtracting 0 from any number gives the number itself as the difference.
When 1 is subtracted from any number, the difference equals the predecessor of the number.
Words like "Minus", "Less", "Difference", "Decrease", "Take Away" and "Deduct" indicate that you need to subtract one number from another.

Topics Related to Subtraction

Check out these interesting articles to know about subtraction and its related topics.

Binary Subtraction
Subtraction Calculator
Addition and Subtraction of Fractions
Subtraction of Complex Numbers
Subtraction of Fractions

Subtraction Examples

Example 1: In an International cricket match, Sri Lanka scored 236 runs and India scored 126 runs. How many more runs should India score to be equal to the number of runs scored by Sri Lanka?

Runs scored by Sri Lanka = 236; Runs scored by India = 126 To find the number of runs that India should score more to be equal to the number of runs scored by Sri Lanka, we will subtract 126 from 236.

H T O 2 3 6 - 1 2 6 1 1 0

Therefore, India must score 110 more runs to be equal to Sri Lanka's runs.

Example 2: Jerry collected 189 seashells and Eva collected 54 shells. Who collected more seashells and by how much?

Number of shells collected by Jerry = 189; Number of shells collected by Eva = 54

This shows that Jerry collected more seashells. Let us subtract 189 - 54 to get the difference.

H T O 1 8 9 - 0 5 4 1 3 5

Therefore, Jerry collected 135 seashells more than Eva.

Example 3: During an annual Easter egg hunt, the participants found 2469 eggs in the clubhouse, out of which 54 Easter eggs were broken. Can you find out the number of unbroken eggs?

The number of easter eggs found in the Clubhouse = 2469; Number of easter eggs that were broken = 54; The total number of unbroken eggs=?

Now, we will subtract the number of broken eggs from the total number of eggs.

Th H T O 2 4 6 9 - 5 4 2 4 1 5

Therefore, the number of unbroken eggs are 2415.

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Practice Questions on Subtraction

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FAQs on Subtraction

Where do we use subtraction.

Subtraction is used in our day-to-day life. For example, if we want to know how much money we spent on the items that we bought, or, how much money is left with us, or, if we want to calculate the time left in finishing a task, we use subtraction.

What Are the Types of Subtraction?

The types of subtraction mean the various methods used in subtraction. For example, subtraction with and without regrouping, subtraction using number charts, subtraction using number line, the subtraction of small numbers using you fingers, and so on.

What Are Subtraction Strategies?

Subtraction strategies are different ways in which subtraction can be learned. For example, using a number line, with the help of a Place Value Chart, separating the Tens and Ones and then subtracting them separately, and many others.

Give Some Subtraction Examples.

There can be various real-life examples of subtraction. For example, if you have 5 apples and your friend ate 3 apples. Using subtraction, we can find out the number of remaining apples: 5 - 3 = 2. So, 2 apples are left with you. Similarly, if there are 16 students in a class, out of which 9 are girls, then we can find out the number of boys in the class by subtracting 9 from 16. (16 - 9 = 7). So, we know that there are 7 boys in the class.

What Are the Three Parts of Subtraction?

The 3 parts of subtraction are named as follows:

Minuend: The number from which we subtract the other number is known as the minuend.
Subtrahend: The number which is subtracted from the minuend is known as the subtrahend.
Difference: The final result obtained after performing subtraction is known as the difference.

How Do You Write a Subtraction?

While writing subtraction, the two important symbols are '-' (minus) and '=' (equal to). The minus sign means when one number is being subtracted from the other number. And the equal to sign delivers the final result.

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Unit 2: Addition and subtraction

About this unit.

In this topic, we will add and subtract whole numbers. The topic starts with 1+1=2 and goes through adding and subtracting within 1000. We will cover regrouping, borrowing, and word problems.

Basic addition and subtraction

Basic addition (Opens a modal)
Basic subtraction (Opens a modal)
Add and subtract: pieces of fruit (Opens a modal)
Relating addition and subtraction (Opens a modal)
Add within 5 7 questions Practice
Subtract within 5 7 questions Practice
Add within 10 7 questions Practice
Subtract within 10 7 questions Practice
Relate addition and subtraction 7 questions Practice
Getting to 10 by filling boxes (Opens a modal)
Adding to 10 (Opens a modal)
Make 10 (grids and number bonds) 7 questions Practice
Make 10 7 questions Practice

Addition and subtraction word problems within 10

Addition word problems within 10 (Opens a modal)
Subtraction word problems within 10 (Opens a modal)
Addition word problems within 10 7 questions Practice
Subtraction word problems within 10 7 questions Practice

Addition and subtraction within 20

Adding within 20 using place value blocks (Opens a modal)
Adding within 20 using ten frames (Opens a modal)
Adding 7 + 6 (Opens a modal)
Adding 8 + 7 (Opens a modal)
Adding with arrays (Opens a modal)
Subtracting different ways (Opens a modal)
Subtract within 20 using a number line (Opens a modal)
Subtract within 20 using place value blocks (Opens a modal)
Subtract within 20 using ten frames (Opens a modal)
Subtracting 14 - 6 (Opens a modal)
Add within 20 visually 7 questions Practice
Add within 20 7 questions Practice
Adding with arrays 4 questions Practice
Subtract within 20 visually 7 questions Practice
Subtract within 20 7 questions Practice
Find missing number (add and subtract within 20) 7 questions Practice
Add & subtract within 20 7 questions Practice

Word problems within 20

Addition and subtraction word problems: superheroes (Opens a modal)
Addition and subtraction word problems: gorillas (Opens a modal)
Addition and subtraction word problems 1 7 questions Practice
Addition and subtraction word problems 2 7 questions Practice
Add and subtract within 20 word problems 7 questions Practice

Word problems with "more" and "fewer"

Comparison word problems: marbles (Opens a modal)
Comparison word problems: roly-polies (Opens a modal)
Word problems with "more" and "fewer" 2 7 questions Practice

Intro to addition with 2-digit numbers

Adding 2-digit numbers without regrouping (Opens a modal)
Adding 2-digit numbers without regrouping 1 (Opens a modal)
Example: Adding 2-digit numbers (no carrying) (Opens a modal)
Breaking apart 2-digit addition problems (Opens a modal)
Regrouping to add 1-digit number (Opens a modal)
Adding up to four 2-digit numbers 4 questions Practice
Break apart 2-digit addition problems 4 questions Practice
Regroup when adding 1-digit numbers 7 questions Practice

Intro to subtraction with 2-digit numbers

Subtracting two-digit numbers without regrouping (Opens a modal)
Subtracting 2-digit numbers without regrouping 1 (Opens a modal)
Subtracting a 1-digit number with regrouping (Opens a modal)
Subtract within 100 using place value blocks 4 questions Practice
Subtract within 100 using a number line 4 questions Practice
Subtract 1-digit numbers with regrouping 7 questions Practice

Strategies for adding and subtracting within 100

Adding 53+17 by making a group of 10 (Opens a modal)
Adding by making a group of 10 (Opens a modal)
Strategies for adding 2-digit numbers (Opens a modal)
Addition and subtraction with number lines (Opens a modal)
Add 2-digit numbers by making tens 4 questions Practice
Add 2-digit numbers by making tens 2 4 questions Practice
Select strategies for adding within 100 4 questions Practice
Add within 100 using a number line 4 questions Practice

Addition within 100

Understanding place value when adding ones (Opens a modal)
Understanding place value when adding tens (Opens a modal)
Adding with regrouping (Opens a modal)
Add within 100 using place value blocks 4 questions Practice

Subtraction within 100

Subtracting with regrouping (borrowing) (Opens a modal)

Word problems within 100

Adding and subtracting on number line word problems (Opens a modal)
Adding two digit numbers on a number line (Opens a modal)
Subtraction word problem: tennis balls (Opens a modal)
Addition word problem: horses (Opens a modal)
Subtraction word problem: snow (Opens a modal)
Subtraction word problem: crayons (Opens a modal)
Multi step addition word problem (Opens a modal)
Multi-step subtraction word problem (Opens a modal)
Add and subtract on the number line word problems 4 questions Practice
Addition word problems within 100 4 questions Practice
Subtraction word problems within 100 4 questions Practice
2-step addition word problems within 100 4 questions Practice
2-step subtraction word problems within 100 4 questions Practice

Adding 1s, 10s, and 100s

Adding 10 or 100 (Opens a modal)
Adding 1s, 10s, and 100s (Opens a modal)
Adding 3-digit numbers (no regrouping) (Opens a modal)
Add 10s and 100s (no regrouping) 4 questions Practice
Add within 1,000 using place value blocks 4 questions Practice

Subtracting 1s, 10s, and 100s

Subtracting 1, 10, or 100 (Opens a modal)
Subtracting 1s, 10s, and 100s (Opens a modal)
Subtracting 3-digit numbers (no regrouping) (Opens a modal)
Subtract 10s and 100s (no regrouping) 7 questions Practice
Subtract within 1,000 using place value blocks 4 questions Practice

Strategies for adding 2- and 3-digit numbers

Breaking apart 3-digit addition problems (Opens a modal)
Solving 3-digit addition in your head (Opens a modal)
Addition using groups of 10 and 100 (Opens a modal)
Adding and subtracting on number line (Opens a modal)
Break apart 3-digit addition problems 4 questions Practice
Add using groups of 10 and 100 4 questions Practice
Add on a number line 4 questions Practice
Select strategies for adding within 1000 4 questions Practice

Addition with regrouping within 1000

Using place value to add 3-digit numbers: part 2 (Opens a modal)
Adding 3-digit numbers (Opens a modal)
Add within 1000 4 questions Practice

Subtraction with regrouping within 1000

Worked example: Subtracting 3-digit numbers (regrouping) (Opens a modal)
Worked example: Subtracting 3-digit numbers (regrouping twice) (Opens a modal)
Worked example: Subtracting 3-digit numbers (regrouping from 0) (Opens a modal)
Subtracting in your head (no regrouping) (Opens a modal)
Subtract on a number line 4 questions Practice
Subtract within 1000 4 questions Practice

Addition and subtraction missing value problems

Missing numbers in addition and subtraction (Opens a modal)
Missing number for 3-digit addition within 1000 (Opens a modal)
Find the missing number (add and subtract within 100) 4 questions Practice
Find the missing number (add and subtract within 1000) 4 questions Practice

Addition and subtraction greater than 1000

Relate place value to standard algorithm for multi-digit addition (Opens a modal)
Multi-digit addition with regrouping (Opens a modal)
Multi-digit subtraction with regrouping: 6798-3359 (Opens a modal)
Multi-digit subtraction with regrouping: 7329-6278 (Opens a modal)
Multi-digit subtraction with regrouping twice (Opens a modal)
Alternate mental subtraction method (Opens a modal)
Adding multi-digit numbers: 48,029+233,930 (Opens a modal)
Relate place value to standard algorithm for multi-digit subtraction (Opens a modal)
Multi-digit subtraction: 389,002-76,151 (Opens a modal)
Multi-digit addition 4 questions Practice
Multi-digit subtraction 4 questions Practice

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Subtraction word problems

In the problem below, Sebastian has 8 pencils and he gives away 5 pencils to his friends. Sebastian is experiencing a loss of 5 pencils, so the subtraction problem to solve to get the answer is 8 - 5 and 8 - 5 = 3.

Sebastian is left with 3 pencils.

Here are a few more interesting subtraction word problems along with their solutions.

A stock bottle of medication contains 500 mg of a drug. You used 125 mg for one prescription and 62.5 mg for a second prescription, while the third prescription was for a child and only 25.25 mg were necessary.

A. What quantity (mg) of the medication has been used? Round to the nearest hundredths.

B. What quantity (mg) of the original medication is left in the stock bottle? Round to the nearest tenths.

A. We can find the quantity that has been used by adding 125 mg, 62.5 mg, and 25.25 mg together.

125 mg + 62.5 + 25.25 = 212.75 mg

212.75 rounded to the nearest hundredths is 212.75

B. We can find the quantity that is left in the stock bottle by subtracting 212.75 mg from 500 mg.

500 - 212.75 = 287.25

287.25 rounded to the nearest tenths is 287.3

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Subtraction Word Problem Worksheets

The extensive set of subtraction word problems featured here will require the learner to find the difference between minuends and subtrahends, which includes problems with regrouping and without regrouping. This large collection of printable word problem worksheets, ideal for children in kindergarten through grade 4 features scenarios that involve single-digit subtraction, two-digit subtraction, three-digit subtraction, and subtraction of large numbers up to six digits. Give yourself a head-start with our free subtraction worksheets!

Word Problems for Beginners: 0 to 10

Find the difference between the numbers that ranges from 0 to 10 in the set of kindergarten worksheets featured here. Use the answer key to verify your responses.

Download the set

Subtraction within 20

Ascend from a beginner to a proficient in performing subtraction up to 20 as you explore this bunch of well-researched word problems and work out the difference within 20.

Two-digit Subtraction: No Regrouping (No Borrowing)

The series of worksheets for grade 1 and grade 2 presented here involve two-digit subtraction word problems that do not require regrouping. Find the differences between the two-digit subtrahends and minuends featured here.

Two-digit Subtraction: Regrouping (Borrowing)

The two-digit subtraction word problems presented in the 2nd grade worksheets here require regrouping (borrowing). Determine the difference between the two-digit numbers by following the place value columns correctly.

Theme based Subtraction Problems

The colorful theme-based worksheet pdfs for kids in 1st grade through 3rd grade are based on three engaging real-life themes - Beach, Italian Ice and Birthday Party.

Three-digit and Two-digit Subtraction

The set of subtraction word problem pdfs featured here will require grade 3 student to find the difference between three-digit minuends and two-digit subtrahends. Use the answer keys to verify your responses.

Three-digit Subtraction Word Problems

Each printable worksheet contains five word problems finding difference between three-digit numbers. Some problems may require regrouping.

Four-digit Subtraction Word Problems

This section contains subtraction word problems on finding the difference between four-digit numbers. Both borrowing and no borrowing problems are included. Some problems may involve subtraction across zero.

Advanced: Large Number Subtraction

The word problems featured in the 4th grade pdf worksheets here include large numbers with minuends and subtrahends up to six digits. Determine the difference between the large numbers by following the place value columns correctly.

Related Worksheets

» Addition Word Problems

» Subtraction within 10

» 2-Digit Subtraction

» Word Problems

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Subtraction Worksheets

Welcome to the Subtraction Worksheets page at Math-Drills.com where you will get less of an experience than our other pages! This page includes Subtraction worksheets on topics such as five minute frenzies, one-, two-, three- and multi-digit subtraction and subtracting across zeros.

Subtraction has been around for several years now... well maybe more than a few, so it's probably a good thing for students to learn. People experience subtraction every minute of their lives from banks and the government taking away your money to the cookies in the jar mysteriously disappearing. With a good knowledge of subtraction, you can understand why your bank account reaches zero and do something to prevent it from happening.

Some students do have difficulty with subtraction, so take it easy on them. Help them to learn their addition facts first. Once they know those, they will need a few more strategies to successfully subtract. Teaching with manipulatives like base ten blocks or cereal or insects in the park can help students gain a deeper understanding of subtraction. The subtracting worksheets on this page are meant to support good teaching practices, so only use them for independent learning if students are practising skills they already know.

We use the words, minuend, subtrahend and difference on this page. Please refer to the following, so you know which word means which part of a subtraction question.

Minuend - Subtrahend = Difference

Most Popular Subtraction Worksheets this Week

$Subtracting 3-Digit from 3-Digit Numbers With Some Regrouping (49 Questions)$

Subtraction Facts Tables

$example of problem solving subtraction$

Five minute subtraction frenzies are timed practice charts that help students develop subtraction fact recall speed. These charts are similar to the addition and multiplication frenzy charts, but due to the nature of how subtraction works, we could not focus solely on the single digit fact families. For example, you might get questions like 18 - 4 = 14. You also have to be aware that you must subtract the row number from the column number to get a positive number (or zero). Other than that, they should be a nice way to practice some mental subtraction. As with most of these pages, please only use them as a timed activity with students who will experience success. If a student does not have the necessary skills to complete a frenzy in under five minutes, you may need to take a different approach to how you deliver this page. For all others, students should be able to complete this page in under five minutes with a 98% or greater accuracy and improve their time as they get more practice.

Five Minute Subtraction Frenzies Five Minute Subtraction Frenzy (Minuends 9 to 18; Subtrahends 0 to 9) Five Minute Subtraction Frenzy (Minuends 29 to 38; Subtrahends 10 to 19) Five Minute Subtraction Frenzy (Minuends 41 to 50; Subtrahends 16 to 25)

Most of the subtraction tables in this section are meant to be used as a reference for students learning their subtraction facts. After a while, most students will remember the facts and recall them easily when completing math problems.

Subtraction Facts Tables 0 to 11 Subtraction Facts 0 to 11 in Grey Subtraction Facts 0 to 11 in Color Subtraction Facts 0 to 11 with Facts Highlighted Subtraction Facts 0 to 11 in Montessori Colors Subtraction Facts 0 to 11 in Montessori Colors with Facts Highlighted
Subtraction Facts Tables 1 to 12 Subtraction Facts Tables in Gray 1 to 12 Subtraction Facts Tables in Color 1 to 12 Subtraction Facts Tables in Montessori Colors 1 to 12 Subtraction Facts 1 to 12 with Facts Highlighted Subtraction Facts 1 to 12 in Montessori Colors with Facts Highlighted
Compact Subtraction Facts Tables Compact Subtraction Table (Filled) Compact Subtraction Table (Blank)

Single-Digit Subtraction Facts

$example of problem solving subtraction$

Subtracting single-digit facts is a skill that students generally learn after or while they are learning single-digit addition facts. The subtraction worksheets in this section are meant to be used for practice, testing or with teacher guidance. They will not teach students how to subtract or what the connection is between addition and subtraction; for that, students require a teacher or parent.

Some students might find it easier to start with subtraction facts with minuends (the first number) limited to 9 or lower. This way, they don't need to count across 10 eliminating that extra pesky digit... for now.

Subtracting Single-Digit from Single-Digit Numbers 100 Subtraction Questions with Minuends up to 9 64 Subtraction Questions with Minuends up to 9 25 Subtraction Questions with Minuends up to 9

In relation to addition facts, the following worksheets cover the facts from 0 to 9, and the worksheets after that cover the addition facts from 1 to 9. The minuends are the amounts to be subtracted from, so a minuend of 18 means that both the subtrahend (the amount being subtracted) and the difference will be 9. The worksheets marked with an asterisk (*) include all possible questions in a random order on each version of the worksheet.

Subtraction Facts from (0 − 0) to (18 − 9) Subtraction Facts from (0 − 0) to (18 − 9) (100* Questions) ✎ Subtraction Facts from (0 − 0) to (18 − 9) (81 Questions) ✎ Subtraction Facts from (0 − 0) to (18 − 9) (64 Questions) ✎ Subtraction Facts from (0 − 0) to (18 − 9) (50 Questions) ✎ Subtraction Facts from (0 − 0) to (18 − 9) (25 Large Print Questions) ✎ Subtraction Facts from (0 − 0) to (18 − 9) (12 Very Large Print Questions) ✎
Subtraction Facts from (2 − 1) to (18 − 9) (No Zeros) Subtraction Facts from (2 − 1) to (18 − 9) (100 Questions) ✎ Subtraction Facts from (2 − 1) to (18 − 9) (81* Questions) ✎ Subtraction Facts from (2 − 1) to (18 − 9) (64 Questions) ✎ Subtraction Facts from (2 − 1) to (18 − 9) (50 Questions) ✎ Subtraction Facts from (2 − 1) to (18 − 9) (25 Large Print Questions) ✎ Subtraction Facts from (2 − 1) to (18 − 9) (12 Very Large Print Questions) ✎
Subtraction Facts with Minuends from 10 to 18 100 Subtraction Questions with Minuends from 10 to 18 and All Regrouping (100 Questions) 64 Subtraction Questions with Minuends from 10 to 18 and All Regrouping (64 Questions) 25 Subtraction Questions with Minuends from 10 to 18 and All Regrouping (25 Large Print Questions)

Sometimes students just need to reinforce a single number at a time which is where these worksheets come in. There are three sets of worksheets in this section, each with a different number of questions. The last set is the most interesting as there are no questions repeated. Eleven and Twelve have been included as they are essentially subtracting by 10 and 1 or 2 more.

Subtracting Individual Focus or Target Facts (50 Questions per Page) Subtracting 0 (50 Questions) ✎ Subtracting 1 (50 Questions) ✎ Subtracting 2 (50 Questions) ✎ Subtracting 3 (50 Questions) ✎ Subtracting 4 (50 Questions) ✎ Subtracting 5 (50 Questions) ✎ Subtracting 6 (50 Questions) ✎ Subtracting 7 (50 Questions) ✎ Subtracting 8 (50 Questions) ✎ Subtracting 9 (50 Questions) ✎ Subtracting 10 (50 Questions) ✎ Subtracting 11 (50 Questions) ✎ Subtracting 12 (50 Questions) ✎
Subtracting Individual Focus or Target Facts (25 Questions per Page) Subtracting Zero (0) (25 Large Print Questions) ✎ Subtracting One (1) (25 Large Print Questions) ✎ Subtracting Two (2) (25 Large Print Questions) ✎ Subtracting Three (3) (25 Large Print Questions) ✎ Subtracting Four (4) (25 Large Print Questions) ✎ Subtracting Five (5) (25 Large Print Questions) ✎ Subtracting Six (6) (25 Large Print Questions) ✎ Subtracting Seven (7) (25 Large Print Questions) ✎ Subtracting Eight (8) (25 Large Print Questions) ✎ Subtracting Nine (9) (25 Large Print Questions) ✎
Subtracting Individual Focus or Target Facts with Differences of 0 to 99 (100 Unique Questions per Page) Subtracting One (1) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Two (2) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Three (3) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Four (4) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Five (5) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Six (6) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Seven (7) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Eight (8) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Nine (9) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Ten (10) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Eleven (11) with Differences 0 to 99 (100 Unique Questions) ✎ Subtracting Twelve (12) with Differences 0 to 99 (100 Unique Questions) ✎
Horizontally Arranged Subtraction Facts with Minuends to 18 Horizontal Subtraction Facts with Minuends to 18 (100 Questions) ✎ Horizontal Subtraction Facts with Minuends to 18 (50 Questions) ✎ Horizontal Subtraction Facts with Minuends to 18 (25 Questions; Large Print) ✎
Horizontally Arranged Subtracting 1 to 5 from 1 to 10 Horizontal Subtracting 1 to 5 from 1 to 10 (100 Questions) ✎ Horizontal Subtracting 1 to 5 from 1 to 10 (50 Questions) ✎ Horizontal Subtracting 1 to 5 from 1 to 10 (25 Questions; Large Print) ✎
Horizontally Arranged Subtracting 1s and 2s from Single-Digit Minuends Horizontal Subtracting Ones from Single-Digit Minuends (25 per page) ✎ Horizontal Subtracting Twos from Single-Digit Minuends (25 per page) ✎
Horizontally Arranged Subtracting Individual Focus Facts Horizontal Subtracting 0s (100 per page) ✎ Horizontal Subtracting 1s (100 per page) ✎ Horizontal Subtracting 2s (100 per page) ✎ Horizontal Subtracting 3s (100 per page) ✎ Horizontal Subtracting 4s (100 per page) ✎ Horizontal Subtracting 5s (100 per page) ✎ Horizontal Subtracting 6s (100 per page) ✎ Horizontal Subtracting 7s (100 per page) ✎ Horizontal Subtracting 8s (100 per page) ✎ Horizontal Subtracting 9s (100 per page) ✎
Horizontally Arranged Subtracting Pairs of Individual Focus Facts Horizontal Subtracting 0s and 1s (100 per page) ✎ Horizontal Subtracting 2s and 3s (100 per page) ✎ Horizontal Subtracting 4s and 5s (100 per page) ✎ Horizontal Subtracting 6s and 7s (100 per page) ✎ Horizontal Subtracting 8s and 9s (100 per page) ✎
Subtracting a Number from Itself Subtracting a Number from Itself (Range 1 to 20)

The make ten subtraction strategy involves "spliting" the subtrahend (amount being subtracted) into two parts. The first part should be the exact amount that will reduce the minuend (the first number) to ten (or multiple of ten as the case may be) and the second part is the leftover amount. The strategy helps students internalize a mental strategy for subtracting across tens. For example, with the question 15 - 9, students first recognize that they need to subtract 5 to get 10, so they split the 9 into 5 and 4. Subtracting 5 from 15 results in 10 and subtracting 4 more results in 6, so 15 - 9 = 6. This strategy can be used any time students need to subtract "over" a multiple of ten and there are many worksheets in this section to practice it. For example, subtracting 84 - 8, students recognize that they must subtract 4 from 84 to get 80 which leaves 4 more to subtract from 80 to get 76.

Make Ten Strategy Worksheets with 10 and Multiples of 10 Make 10 Subtraction Strategy Make 20 Subtraction Strategy Make 30 Subtraction Strategy Make 40 Subtraction Strategy Make 50 Subtraction Strategy Make 60 Subtraction Strategy Make 70 Subtraction Strategy Make 80 Subtraction Strategy Make 90 Subtraction Strategy Make Multiples of 10 Subtraction Strategy

Long Subtraction Worksheets

$example of problem solving subtraction$

Try teaching a mental math strategy for subtraction called counting up. Here is how it is done:

Start with the second number (the subtrahend) and count up by tens until you find the closest value to the first number (the minuend). Keep track of how many tens you counted. Add or subtract a single digit number to get the minuend exactly then adjust the tens by that amount. For the question, 84 - 35, start at 35, and count, 45, 55, 65, 75, 85 (five tens) and one down to get 84. Five tens minus one is 49. For the question 65 - 22, start at 22 and count, 32, 42, 52, 62 (four tens) and three up to get 65. Four tens and three is 43. The previous examples used two-digit numbers, but the strategy can swiftly be modified for larger numbers. How far can your students go with it? Here is an example with three-digit numbers:

Let's use the question 927 - 648. First, count up by hundreds to 948 (that's 300). Then count down by tens to 928 (that's -20). Finally count down by ones to 927 (that's one). 300 - 20 - 1 = 279. That's almost easier than adding!

The multi-digit or long subtraction worksheets in the first part of this section are classic long subtraction worksheets with randomly generated numbers. Regrouping should be necessary about half of the time. Versions with ALL regrouping and NO regrouping follow. If you would like to see numbers with thousands separators, look a little further down and choose the appropriate version for your location.

Subtracting up to 3-Digit Numbers with Some Regrouping Subtracting 2-Digit from 2-Digit Numbers with Some Regrouping ✎ Subtracting 2-Digit from 3-Digit Numbers with Some Regrouping ✎ Subtracting 3-Digit from 3-Digit Numbers with Some Regrouping ✎ 3-Digit Expanded Form Subtraction Subtracting 3-Digit from 4-Digit Numbers with Some Regrouping ✎
Subtracting up to 3-Digit Numbers with Some Regrouping (Large Print) Subtracting 1-Digit from 2-Digit Numbers with Some Regrouping ( Large Print ) ✎ Subtracting 2-Digit from 2-Digit Numbers with Some Regrouping ( Large Print ) ✎ Subtracting 1-Digit from 3-Digit Numbers with Some Regrouping ( Large Print ) ✎ Subtracting 2-Digit from 3-Digit Numbers with Some Regrouping ( Large Print ) ✎ Subtracting 3-Digit from 3-Digit Numbers with Some Regrouping ( Large Print ) ✎ Subtracting 1- to 3-Digit from 1- to 3-Digit Numbers with Some Regrouping ( Large Print ) ✎ Subtracting 3-Digit from 4-Digit Numbers with Some Regrouping ( Large Print ) ✎
Subtracting 4- to 9-Digit Numbers with Some Regrouping Subtracting 4-Digit from 4-Digit Numbers with Some Regrouping ✎ Subtracting 4-Digit from 5-Digit Numbers with Some Regrouping ✎ Subtracting 5-Digit from 5-Digit Numbers with Some Regrouping ✎ Subtracting 5-Digit from 6-Digit Numbers with Some Regrouping ✎ Subtracting 6-Digit from 6-Digit Numbers with Some Regrouping ✎ Subtracting 6-Digit from 7-Digit Numbers with Some Regrouping ✎ Subtracting 7-Digit from 7-Digit Numbers with Some Regrouping ✎ Subtracting 7-Digit from 8-Digit Numbers with Some Regrouping ✎ Subtracting 8-Digit from 8-Digit Numbers with Some Regrouping ✎ Subtracting 8-Digit from 9-Digit Numbers with Some Regrouping ✎ Subtracting 9-Digit from 9-Digit Numbers with Some Regrouping ✎
Subtracting 4- to 6-Digit Numbers with Some Regrouping (Large Print) Subtracting 4-Digit from 4-Digit Numbers with Some Regrouping ( Large Print ) ✎ Subtracting 4-Digit from 5-Digit Numbers with Some Regrouping ( Large Print ) ✎ Subtracting 5-Digit from 5-Digit Numbers with Some Regrouping ( Large Print ) ✎ Subtracting 5-Digit from 6-Digit Numbers with Some Regrouping ( Large Print ) ✎ Subtracting 6-Digit from 6-Digit Numbers with Some Regrouping ( Large Print ) ✎

For students who need a little extra help with lining things up, these long subtraction worksheets have the digits spaced farther apart on a grid. The answer keys also show the carrying values to help diagnose where things went wrong (but hopefully they won't).

Long Subtraction Worksheets with Grid Support 2-Digit Minus 2-Digit Subtraction With Grid Support 3-Digit Minus 2-Digit Subtraction With Grid Support 3-Digit Minus 3-Digit Subtraction With Grid Support 4-Digit Minus 3-Digit Subtraction With Grid Support 4-Digit Minus 4-Digit Subtraction With Grid Support 5-Digit Minus 4-Digit Subtraction With Grid Support 5-Digit Minus 5-Digit Subtraction With Grid Support 6-Digit Minus 5-Digit Subtraction With Grid Support 6-Digit Minus 6-Digit Subtraction With Grid Support 2- to 4-Digit Minus 2- to 4-Digit Subtraction With Grid Support 3- to 6-Digit Minus 3- to 6-Digit Subtraction With Grid Support

The next long subtraction worksheets include questions that require regrouping at every step. They can be frustrating and difficult for students who are not familiar with the concept of subtraction. Try showing them with base ten blocks how regrouping works.

Subtracting up to 3-Digit Numbers with All Regrouping Subtracting 1-Digit Numbers with ALL Regrouping ✎ Subtracting 2-Digit Numbers with ALL Regrouping ✎ Subtracting 3-Digit Numbers with ALL Regrouping ✎
Subtracting up to 3-Digit Numbers with All Regrouping (Large Print) Subtracting 1-Digit Numbers with ALL Regrouping ( Large Print ) ✎ Subtracting 2-Digit Numbers with ALL Regrouping ( Large Print ) ✎ Subtracting 3-Digit Numbers with ALL Regrouping ( Large Print ) ✎
Subtracting 4- to 8-Digit Numbers with All Regrouping Subtracting 4-Digit Numbers with ALL Regrouping ✎ Subtracting 5-Digit Numbers with ALL Regrouping ✎ Subtracting 6-Digit Numbers with ALL Regrouping ✎ Subtracting 7-Digit Numbers with ALL Regrouping ✎ Subtracting 8-Digit Numbers with ALL Regrouping ✎
Subtracting 4- to 6-Digit Numbers with All Regrouping (Large Print) Subtracting 4-Digit Numbers with ALL Regrouping ( Large Print ) ✎ Subtracting 5-Digit Numbers with ALL Regrouping ( Large Print ) ✎ Subtracting 6-Digit Numbers with ALL Regrouping ( Large Print ) ✎

Some students require a little extra help when learning to subtract large numbers. These subtraction worksheets include questions where the regrouping step has been eliminated. This might help students learn a subtraction algorithm before learning about regrouping.

Subtracting up to 3-Digit Numbers with No Regrouping Subtracting 2-Digit from 2-Digit Numbers with NO Regrouping ✎ Subtracting 2-Digit from 3-Digit Numbers with NO Regrouping ✎ Subtracting 3-Digit from 3-Digit Numbers with NO Regrouping ✎ Subtracting 2-Digit from 4-Digit Numbers with NO Regrouping ✎ Subtracting 3-Digit from 4-Digit Numbers with NO Regrouping ✎
Subtracting up to 3-Digit Numbers with No Regrouping (Large Print) Subtracting 2-Digit from 2-Digit Numbers with NO Regrouping ( Large Print ) ✎ Subtracting 2-Digit from 3-Digit Numbers with NO Regrouping ( Large Print ) ✎ Subtracting 3-Digit from 3-Digit Numbers with NO Regrouping ( Large Print ) ✎ Subtracting 2-Digit from 4-Digit Numbers with NO Regrouping ( Large Print ) ✎ Subtracting 3-Digit from 4-Digit Numbers with NO Regrouping ( Large Print ) ✎
Subtracting 4- to 9-Digit Numbers with No Regrouping Subtracting 4-Digit from 4-Digit Numbers with NO Regrouping ✎ Subtracting 5-Digit from 5-Digit Numbers with NO Regrouping ✎ Subtracting 6-Digit from 6-Digit Numbers with NO Regrouping ✎ Subtracting 7-Digit from 7-Digit Numbers with NO Regrouping ✎ Subtracting 8-Digit from 8-Digit Numbers with NO Regrouping ✎ Subtracting 9-Digit from 9-Digit Numbers with NO Regrouping ✎
Subtracting 4- to 6-Digit Numbers with No Regrouping (Large Print) Subtracting 4-Digit from 4-Digit Numbers with NO Regrouping ( Large Print ) ✎ Subtracting 5-Digit from 5-Digit Numbers with NO Regrouping ( Large Print ) ✎ Subtracting 6-Digit from 6-Digit Numbers with NO Regrouping ( Large Print ) ✎

Why horizontal subtraction worksheets? Students can show their understanding of place value and number sense if they do not already have the numbers lined up. Vertical subtraction is often learned based on a student's understanding of single-digit subtraction, but looking at the whole number is lost in the algorithm.

Horizontally Arranged 2-Digit Minus 1-Digit Questions 2-digit Minus 1-Digit Horizontal Subtraction (100 Questions) ✎ 2-digit Minus 1-Digit Horizontal Subtraction (50 Questions) ✎ 2-digit Minus 1-Digit Horizontal Subtraction (25 Questions; Large Print) ✎
Horizontally Arranged 2-Digit Minus 2-Digit Questions 2-digit Minus 2-Digit Horizontal Subtraction (100 Questions) ✎ 2-digit Minus 2-Digit Horizontal Subtraction (50 Questions) ✎ 2-digit Minus 2-Digit Horizontal Subtraction (25 Questions; Large Print) ✎
Horizontally Arranged 3-Digit Minus 1-Digit Questions 3-digit Minus 1-Digit Horizontal Subtraction (100 Questions) ✎ 3-digit Minus 1-Digit Horizontal Subtraction (50 Questions) ✎ 3-digit Minus 1-Digit Horizontal Subtraction (25 Questions; Large Print) ✎
Horizontally Arranged 3-Digit Minus 2-Digit Questions 3-digit Minus 2-Digit Horizontal Subtraction (50 Questions) ✎ 3-digit Minus 2-Digit Horizontal Subtraction (25 Questions; Large Print) ✎ 3-Digit Minus 2-Digit Horizontal Subtraction ( All Regrouping ; 100 Questions)
Horizontally Arranged 3-Digit Minus 3-Digit Questions 3-Digit Minus 3-Digit Horizontal Subtraction (50 Questions) ✎ 3-Digit Minus 3-Digit Horizontal Subtraction (25 Questions; Large Print) ✎
Horizontally Arranged Various-Digit Minus Various-Digit Questions Various-Digit Minus Various-Digit Horizontal Subtraction (50 Questions) ✎ Various-Digit Minus Various-Digit Horizontal Subtraction (25 Questions; Large Print) ✎

Many students in English-speaking countries are used to seeing numbers with comma-separated thousands.

Long Subtraction Worksheets with Comma Separated Thousands Subtracting 2-Digit from 4-Digit Numbers (Comma Separated) ✎ Subtracting 3-Digit from 4-Digit Numbers (Comma Separated) ✎ Subtracting 4-Digit from 4-Digit Numbers (Comma Separated) ✎ Subtracting 2-Digit from 5-Digit Numbers (Comma Separated) ✎ Subtracting 3-Digit from 5-Digit Numbers (Comma Separated) ✎ Subtracting 4-Digit from 5-Digit Numbers (Comma Separated) ✎ Subtracting 5-Digit from 5-Digit Numbers (Comma Separated) ✎ Mixture of Multi-Digit Subtraction from 2 to 4 digits (Comma Separated) ✎ Mixture of Multi-Digit Subtraction from 2 to 5 digits (Comma Separated) ✎
Long Subtraction Worksheets with Comma Separated Thousands and All Regrouping Subtracting 4-Digit Numbers with ALL Regrouping (Comma Separated) ✎ Subtracting 5-Digit Numbers with ALL Regrouping (Comma Separated) ✎ Subtracting 6-Digit Numbers with ALL Regrouping (Comma Separated) ✎ Subtracting 7-Digit Numbers with ALL Regrouping (Comma Separated) ✎ Subtracting 8-Digit Numbers with ALL Regrouping (Comma Separated) ✎
Long Subtraction Worksheets with Comma Separated Thousands and No Regrouping Subtracting 5-Digit from 5-Digit Numbers with NO Regrouping (Comma Separated) ✎ Subtracting 6-Digit from 6-Digit Numbers with NO Regrouping (Comma Separated) ✎ Subtracting 7-Digit from 7-Digit Numbers with NO Regrouping (Comma Separated) ✎ Subtracting 8-Digit from 8-Digit Numbers with NO Regrouping (Comma Separated) ✎ Subtracting 9-Digit from 9-Digit Numbers with NO Regrouping (Comma Separated) ✎

Space-separated thousands are becoming more widely used, including in the United States. Canadian students have used both comma separated and space separated thousands for many years.

Long Subtraction Worksheets with Space Separated Thousands Subtracting 2-Digit from 4-Digit Numbers (Space Separated) ✎ Subtracting 3-Digit from 4-Digit Numbers (Space Separated) ✎ Subtracting 4-Digit from 4-Digit Numbers (Space Separated) ✎ Subtracting 2-Digit from 5-Digit Numbers (Space Separated) ✎ Subtracting 3-Digit from 5-Digit Numbers (Space Separated) ✎ Subtracting 4-Digit from 5-Digit Numbers (Space Separated) ✎ Subtracting 5-Digit from 5-Digit Numbers (Space Separated) ✎ Mixture of Multi-Digit Subtraction from 2 to 4 digits (Space Separated) ✎ Mixture of Multi-Digit Subtraction from 2 to 5 digits (Space Separated) ✎
Long Subtraction Worksheets with Space Separated Thousands and All Regrouping Subtracting 4-Digit Numbers with ALL Regrouping (Space Separated) ✎ Subtracting 5-Digit Numbers with ALL Regrouping (Space Separated) ✎ Subtracting 6-Digit Numbers with ALL Regrouping (Space Separated) ✎ Subtracting 7-Digit Numbers with ALL Regrouping (Space Separated) ✎ Subtracting 8-Digit Numbers with ALL Regrouping (Space Separated) ✎
Long Subtraction Worksheets with Space Separated Thousands and No Regrouping Subtracting 5-Digit from 5-Digit Numbers with NO Regrouping (Space Separated) ✎ Subtracting 6-Digit from 6-Digit Numbers with NO Regrouping (Space Separated) ✎ Subtracting 7-Digit from 7-Digit Numbers with NO Regrouping (Space Separated) ✎ Subtracting 8-Digit from 8-Digit Numbers with NO Regrouping (Space Separated) ✎ Subtracting 9-Digit from 9-Digit Numbers with NO Regrouping (Space Separated) ✎

Even though period separated thousands are not common in the English-speaking world, we provide these for our friends in other countries who may find them useful.

Long Subtraction Worksheets with Period Separated Thousands Subtracting 2-Digit from 4-Digit Numbers (Period Separated) ✎ Subtracting 3-Digit from 4-Digit Numbers (Period Separated) ✎ Subtracting 4-Digit from 4-Digit Numbers (Period Separated) ✎ Subtracting 2-Digit from 5-Digit Numbers (Period Separated) ✎ Subtracting 3-Digit from 5-Digit Numbers (Period Separated) ✎ Subtracting 4-Digit from 5-Digit Numbers (Period Separated) ✎ Subtracting 5-Digit from 5-Digit Numbers (Period Separated) ✎ Mixture of Multi-Digit Subtraction from 2 to 4 digits (Period Separated) ✎ Mixture of Multi-Digit Subtraction from 2 to 5 digits (Period Separated) ✎
Long Subtraction Worksheets with Period Separated Thousands and All Regrouping Subtracting 4-Digit Numbers with ALL Regrouping (Period Separated) ✎ Subtracting 5-Digit Numbers with ALL Regrouping (Period Separated) ✎ Subtracting 6-Digit Numbers with ALL Regrouping (Period Separated) ✎ Subtracting 7-Digit Numbers with ALL Regrouping (Period Separated) ✎ Subtracting 8-Digit Numbers with ALL Regrouping (Period Separated) ✎
Long Subtraction Worksheets with Period Separated Thousands and No Regrouping Subtracting 5-Digit from 5-Digit Numbers with NO Regrouping (Period Separated) ✎ Subtracting 6-Digit from 6-Digit Numbers with NO Regrouping (Period Separated) ✎ Subtracting 7-Digit from 7-Digit Numbers with NO Regrouping (Period Separated) ✎ Subtracting 8-Digit from 8-Digit Numbers with NO Regrouping (Period Separated) ✎ Subtracting 9-Digit from 9-Digit Numbers with NO Regrouping (Period Separated) ✎

Various Other Long Subtraction Worksheets

$example of problem solving subtraction$

Generally, a student would not regroup to determine the complements of 10, 100, 1000, etc. One strategy that could be used is as follows: working from left to right, a student would take each digit in the subtrahend and figure out its nines complement. If the digit was 3, for example, the nines complement of 3 is 6. For the last digit (ones), the student would use the tens complement. For example, a typical question is 1000 - 456. The nines complement of 4 is 5, the nines complement of 5 is 4 and the tens complement of 6 is 4. Putting it all together, the student would get 5 4 4 or 544 = 1000 - 456.

Calculating Complements of Powers of Ten (Subtracting Across Zeros) Complements of 10 Complements of 100 Complements of 1000 Complements of 10000 Complements of 100 and 1000 Complements of 1000 and 10000 Complements of 100, 1000 and 10000

A similar strategy is employed with the next worksheets except students must adapt to calculating the largest place value number.

Calculating Complements of Multiples of Powers of Ten (Subtracting Across Zeros) Subtracting from multiples of 10 Subtracting from multiples of 100 Subtracting from multiples of 1000 Subtracting from multiples of 10000 Subtracting from a mixture of multiples of 100 and 1000 Subtracting from a mixture of multiples of 1000 and 10000 Subtracting from a mixture of multiples of 100, 1000 and 10000

These worksheets are meant to give students practice dealing with 0's in the middles of subtraction questions. Whether using pencil and paper or mental arithmetic, it is always a good idea to make sure students know what to do when they encounter zeros.

Subtracting Across Zeros in the Middle (Ones Always Need Regrouping) 3-Digit Subtraction across zeros in the middle ( Ones always need regrouping ) 4-Digit Subtraction across zeros in the middle ( Ones always need regrouping ) 5-Digit Subtraction across zeros in the middle ( Ones always need regrouping )
Subtracting Across Zeros in the Middle (Ones Sometimes Need Regrouping) 3-Digit Subtraction across zeros in the middle ( Ones sometimes need regrouping ) 4-Digit Subtraction across zeros in the middle ( Ones sometimes need regrouping ) 5-Digit Subtraction across zeros in the middle ( Ones sometimes need regrouping )

Subtracting numbers in number systems other than decimal numbers including binary, quaternary, octal, duodecimal and hexadecimal numbers.

Subtracting in Other Base Number Systems Subtracting Binary Numbers (Base 2) Subtracting Ternary Numbers (Base 3) Subtracting Quaternary Numbers (Base 4) Subtracting Quinary Numbers (Base 5) Subtracting Senary Numbers (Base 6) Subtracting Octal Numbers (Base 8) Subtracting Duodecimal Numbers (Base 12) Subtracting Hexadecimal Numbers (Base 16) Subtracting Vigesimal Numbers (Base 20) Subtracting Hexatrigesimal Numbers (Base 36) Subtracting Various Numbers (Various Bases)

Subtraction – Definition, Symbol, Examples, Practice Problems

What is subtraction in math, symbol of subtraction, regrouping in math, solved examples on subtraction, practice problems on subtraction, frequently asked questions on subtraction, subtraction: introduction.

Suppose we purchase ice cream for a certain amount of money, say $\$140$, and we give $\$200$ to the cashier. Now, the cashier returns the excess amount by performing subtraction such as $200 − 140 = 60$. Then, the cashier will return $\$60$.

What is exactly happening here?

The answer to this question is subtraction.

Break into Tens and Ones to Subtract Game

Subtraction is one of the four basic arithmetic operations in mathematics. The other three being addition , multiplication , and division .

We can observe the applications of subtraction in our day-to-day life in different situations.

For example, if we have 3 candies and our friend asks us for 1 candy, how many candies are we left with? Simply,

$3 − 1 = 2$

Let’s understand the concept with the help of the following example of apples.

$Subtraction using objects$

In the example above, if Harry has 6 apples and he gives 3 apples to Jim, How many apples are left with him?

We can calculate this by subtracting 3 from 6:

$6 − 3 = 3$

Harry is left with 3 apples.

Related Worksheets

$Add & Subtract Multiples of 10 Worksheet$

Definition of Subtraction

The operation or process of finding the difference between two numbers or quantities is known as subtraction. To subtract a number from another number is also referred to as ‘taking away one number from another’. Some instances where we use subtraction are while making payments, transferring money to our friends and many more.

In mathematics, we have generally used different symbols for different operators. We have symbols like $+, −, /, *$ and many more. The subtraction symbol $“−”$ is one of the most important math symbols that we use. In the above section, we read about subtracting two numbers 6 and 3. If we observe this expression: $(6 − 3 = 3)$, the symbol $(−)$ between the two numbers is what denotes subtraction. This symbol is also known as the minus $(−)$ sign.

Formula of Subtraction Operation

When we subtract two numbers, we commonly use some terms that are used in a subtraction expression:

Minuend : A minuend is the number from which the other number is subtracted.

Subtrahend : A subtrahend is the number which is to be subtracted from the minuend.

Difference : A difference is the final result after subtracting the subtrahend from the minuend.

$minuend, subtrahend and difference example$

The subtraction formula is written as

Minuend $−$ Subtrahend $=$ Difference

For example,

$7 − 3 = 4$

Here,

$7 =$ Minuend

$3 =$ Subtrahend

$4 =$ Difference

What Is Minus in Math?

Minus is a sign or a symbol that is represented by a horizontal line .

$Minus sign$

We use minus in mathematics for multiple representations.

Uses of Minus Sign

Subtraction operation.

Minus represents the arithmetic operation of subtraction between two numbers. We use minus sign to denote subtract, decreased by, take away, etc.

For example,

$Subtraction operation$

Minus sign also means how much is one value more than the other value.

For example, Darby has 8 gingerbread with her and Olive has 3 gingerbreads.

Darby has more gingerbreads by $(8 − 3) = 5$

$Minus symbol used in example$

To Represent Negative Integers

Integers are the numbers that are not in decimal or fractional form and include positive and negative numbers along with 0. We use the minus sign to represent the negative integers, i.e., the whole numbers which are less than zero (no fractions).

For representing a negative integer, we add a negative or minus sign in front of a whole number. For example, negative integer 5 is represented as: $(− 5)$

Use in Measurement

We also use the minus sign in measurement specially in temperature.

For example, a temperature of $− 4^{\circ} \text{C}$ means 4 degrees below zero.

Another example: The temperature is $5^{\circ} \text{C}$ and then drops $− 10^{\circ} \text{C}$. What is the temperature now?

The temperature now $= 5 − 10 = − 5^{\circ} \text{C}$

$Minus sign for temperature measurement$

To Represent Opposite Directions

We also use the minus sign to represent a negative direction on a graph paper to show the coordinates.

$Negative direction on coordinate plane$

The graph also runs in the negative direction.

In the first quadrant, the coordinates are of the form $(x,y)$.
In the second quadrant, the coordinates are of the form $(−x,y)$.
In the third quadrant, the coordinates are of the form $(−x,−y)$.
In the fourth quadrant, the coordinates are of the form $(x,−y)$.

Mathematical Operations on Integers Using “Minus” Sign

Multiplication of two negative numbers gives a positive number.

Negative $\times$ Negative $=$ Positive

For example, $(− 5) \times (− 15) = + 75$

Multiplication of a negative number and a positive number gives a negative number.

Negative $\times$ Positive $=$ Negative

For example, $(− 5) \times (15) = − 75$

Addition of a negative number with a negative number will always give a negative number.

Negative $+$ Negative $=$ Negative

For example, $(− 3) + (− 4) = (− 7)$

Subtracting a positive number from a negative number will always give a negative number.

If we subtract a positive number from a negative number, we start at the negative number and count backwards.

Negative $−$ Positive $=$ Negative

Using the number line, let’s start at $− 3$.

For example: Say, we have the problem $(− 2) − 3$.

$Number line subtraction$

Now count backwards 3 units. So, keep counting back three spaces from $− 2$ on the number line, we get

$Subtraction on number line$

The answer is $(− 2) − 3 = − 5$.

Subtracting a negative number from a negative number

A negative sign followed by a negative sign, turns the two signs into a positive sign. So, instead of subtracting a negative, you are adding a positive. The answer could be either positive or negative, depending on the magnitude of the numbers.

Negative $−$ Negative $=$ Negative $+$ Positive

Basically, $− (− 5)$ becomes $+ 5$, and then you add the numbers.

For example, we have $(− 2) − (− 5)$. We can read it as “negative two minus negative 5”. We’re changing the two negative signs into a positive, so the equation now becomes $(− 2) + 5$.

On the number line, it starts at $− 2$.

$Negative numbers on a number line$

Then we move forward 5 units: $+ 5$.

$Subtracting 2 negative numbers on a number line$

The answer is $− 2 − (− 5) = 3$.

Subtracting a negative number from a positive number will always give a positive number.

When we subtract a negative number from a positive number, we turn the subtraction sign followed by a negative sign into a plus sign. So, instead of subtracting a negative, you’re adding a positive. So the equation turns into a simple addition problem.

Positive – Negative = Positive + Positive

For example, let’s say we have the problem $2 − (− 4)$. This reads “two minus negative four.” The $− (− 4)$ turns into $+ 4$.

On the number line we start at 2.

$Subtracting on a number line$

Then we move forward three units: $2 + 4$.

$Subtracting 2 numbers on a number line$

The answer is $2 − (− 4) = 6$.

Methods of Subtraction

There are various methods for subtraction. In this article, we shall be discussing three of them.

Visual representation

One of the methods is to use a diagram showing what you start with, what you are taking away, and what you are left with.

For example, we have 5 balls, now a friend asks for 2 balls, we can easily calculate that we are left with 2 balls using the concept of subtraction by depicting it through a diagram as given below:

$Diagram for subtracting visually$

Another method to perform subtraction is by using a number line.

Subtraction on Number Lines

If we want to calculate 5 minus 2, we start from 5. Since we need to subtract 2, we take 2 steps back. Finally we observe that we are standing at 3.

So, this is how $5 − 2$ is calculated on the number line.

$Subtraction using number line$

This is a number line representation of the expression.

Column method

The generally used method is the column method of subtraction, where we separate the numbers into ones, tens, hundreds and so on and write the minuend above the subtrahend, where all the ones are in one column, all the tens are in another column and so on. In this method, we always start the subtraction with the ones and proceed from right to left.

$Subtraction using columns$

Regrouping in math can be defined as the process of making/breaking groups when carrying out operations like addition and subtraction. To regroup means to rearrange groups in place value to carry out an operation. We use regrouping in subtraction, when digits in the minuend are smaller than the digits in the same place of the subtrahend.

This process is called regrouping as we are regrouping numbers or rearranging them into their place value to carry out this process. When we use regrouping in subtraction, it is also sometimes called borrowing.

Subtraction with Regrouping

In subtraction, we sometimes use the concept of regrouping between numbers. When the numbers are subtracted using the column method and the bottom digit is greater than the upper digit, we regroup the numbers to be able to subtract.

Let us understand subtraction using this regrouping example, which includes finding the answer to the expression $31 − 19$.

$Regrouping to subtract$

Here, we first subtract the unit place digit of the number in the lower slot with the upper slot. If the number in the lower slot is larger than the number in the upper slot, regrouping takes place, also called borrowing. In this case, we subtract one from the tens place digit from the upper slot number and write the remaining number above it, that is, we take 1 from 3 making it 2 which we wrote above 3, while this 1 that we subtracted is “borrowed” to the unit place, making it a 10 and adding it to the unit place existing number, giving us a two digit number. In simpler words 10 is borrowed from the tens place digit and added to the unit place digit. In the above example, 10 is added to the unit place digit i.e. 1 and we write 11 above the unit place digit.

$Regrouping to subtract numbers$

Now, we move on to the real subtraction of the two numbers. The number of the unit place of the upper slot can now be subtracted from the unit place number of the lower slot, i.e. $11 − 9$ giving us 2. While we normally take the remaining number from the upper slot i.e. 2 and subtract the lower slot number from it, i.e., $2 − 1$, giving us 1, which leaves us with 12 as the final answer.

$Regrouping for subtraction$

Here’s how we regroup hundred and tens to subtract 182 from 427:

$regrouping hundreds to subtract$

Properties of Subtraction

Here are a few important properties of subtraction in our everyday life.

Commutative property of subtraction:

Commutative property states that swapping of numbers does not alter the result. But in subtraction, we cannot get the same output when we put minuend in place of subtrahend and vice versa. Hence, commutative property is not possible in case of subtraction.

For example, $8 − 5$ is not equal to $5 − 8$.

Identity property of subtraction:

Identity property states that when we subtract “0” from a number, the resultant is the number itself.

For example, $5 − 0 = 5$.

Inverse Property of Subtraction (Subtracting a number by itself):

When we subtract a number from itself, the resultant is always “0.”

$\text{A} − \text{A} = 0$

For example, $9 − 9 = 0$.

Subtraction Property of Equality

According to the property, if we subtract any number on both sides of an equation, the equality of the equation still holds.

For the given algebra equation;

$\Rightarrow \times − 3 = 5$

If we subtract the same number on both sides, the equation will still hold true. Here we will subtract 8 from both sides.

$\Rightarrow \times − 3 − 8 = 5 − 8$

$\Rightarrow \times − 11 = − 3$

Distributive Property of Subtraction

According to the property, the multiplication of subtraction of numbers is equal to subtraction of the multiplication of individual numbers.

$\text{A} \times (\text{B} − \text{C}) = \text{A} \times \text{B} − \text{A} \times \text{C}$

For example: $3 \times (5 − 2) = 3 \times 3 = 9$ and $3 \times 5 − 3 \times 2 = 15 − 6 = 9$

In this article, we have learned about subtraction, its definition with example, the symbols used for it, the common methods used for subtraction. We also learned about the minus sign. The minus sign is used for different purposes. Let’s practice our understanding with a few solved examples and practice problems and solved examples.

1. In a soccer match, Team A scored 5 goals and Team B scored 9 goals. Which team scored more goals and by how much?

Goals scored by Team $\text{A} = 5$;

Goals scored by Team $\text{B} = 9$

We can clearly see that Team B scored more goals. To calculate the numbers of goals by which Team B exceeded, we will subtract 5 from 9.

$9 − 5 = 4$

Therefore, Team B scored 4 more goals than Team A.

2. Jeff has 120 pens. Her friend Tim has 50 pens less than Jeff. How many pens does Tim have?

As we know, the term “less than” refers to the operation subtraction.

Jeff $= 120$

Tim $= 120 − 50 = 70$

Therefore, Tim has 70 pens.

3. During an annual Easter egg hunt, the participants found 52 eggs in the clubhouse, out of which 14 Easter eggs were broken. Can you find out the exact number of unbroken eggs?

The number of easter eggs found in the Clubhouse $= 52$;

Number of easter eggs that were broken $= 14$;

The total number of unbroken eggs $=$ ?

Now, we will subtract the number of broken eggs from the total number of eggs.

$Subtracting 14 from 52$

Therefore, the number of unbroken eggs is 38.

4. Jerry collected 194 fishes and Evan collected 132 fishes. Who collected more fish and by how much?

Number of fishes collected by Jerry $= 194$;

Number of fishes collected by Evan $= 132$

This shows that Jerry collected more fish. Let us subtract $194 − 132$ to get the difference.

$Subtraction word problem$

Therefore, Jerry collected 62 fish more than Evan.

5. By how much is 5251 less than 6556?

From the given, it is clear that 6556 is greater than 5251 .

Now subtract 5251 from 6556.

$Subtracting large numbers example$

$6556 − 5251 = 1305$

Therefore, 5251 is less than 6556 by 1305.

6. What is the value of 794 minus 658?

Solution: $794 − 658 = 136$

7. When Steve woke up, his temperature was $101^{\circ} \text{F}$ . Two hours later, it was 3º lower. What was his temperature after two hours?

Solution: Temperature at the time of Steve waking up $= 101^{\circ} \text{F}$

Temperature after 2 hours $= 101^{\circ} \text{F} − 3^{\circ} \text{F} = 98^{\circ} \text{F}$

8. What will be the coordinates of A if $x = −5$ and $y = − 7$ . In which quadrant will A lie?

Solution: Since it is given that $x = − 5$ and $y = − 7$, the coordinates of A will be $(− 5, − 7)$. Also, as both the coordinates are negative, i.e., $( − x, − y)$, A will lie in the third quadrant.

9. An elevator is on the eighteenth floor. It goes down 13 floors. What floor is the elevator on now?

Solution: The floor on which the elevator is now $= 18 − 13 = 5$th floor

10. Is $(4 − 6) = (6 − 4)$ ?

Solution: Let us find the solution to both of them.

On the left side, $4 − 6 = − 2$

Whereas, on the right side, $6 − 4 = 2$

We can clearly see that $2 \neq − 2$.

So, $(4 − 6)$ is not equal to $(6 − 4)$.